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Solving Radical Equations & Finding Unknown Values

Learn how to solve radical equations and find unknown values using various methods. Practice solving equations involving radicals and explore real-life application problems.

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Solving Radical Equations & Finding Unknown Values

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  1. Warm Up(Add to Hw) • Solve each equation. • 1. 3x +5 = 17 • 2. 4x + 1 = 2x – 3 • 3. • 4. (x + 7)(x – 4) = 0 • 5. x2 – 11x + 30 = 0 4 –2 35 –7, 4 6, 5

  2. 11-9 Solving Radical Equations Holt Algebra 1

  3. A radical equation is an equation that contains a variable within a radical.

  4. Check 5 5 5 Example 1A: Solving Simple Radical Equations Solve the equation. Check your answer. Square both sides. x = 25 Substitute 25 for x in the original equation.  Simplify.

  5. Check  Check It Out! Example 1b Solve the equation. Check your answer. Square both sides. 81 = 27x Divide both sides by 27. 3 = x Substitute 3 for x in the original equation. Simplify.

  6. Check Example 2A: Solving Simple Radical Equations Solve the equation. Check your answer. Add 4 to both sides. Square both sides. x = 81 9 – 4 5  5 5

  7. Check  7 7 Example 2B: Solving Simple Radical Equations Solve the equation. Check your answer. Square both sides. x = 46 Subtract 3 from both sides.

  8. Example 2C: Solving Simple Radical Equations Solve the equation. Check your answer. Subtract 6 from both sides. Square both sides. 5x + 1 = 16 5x = 15 Subtract 1 from both sides. x = 3 Divide both sides by 5.

  9. Example 3A: Solving Radical Equations by Multiplying or Dividing Solve the equation. Check your answer. Divide both sides by 4. Square both sides. x = 64

  10. Example 3B: Solving Radical Equations by Multiplying or Dividing Solve the equation. Check your answer. Multiply both sides by 2. Square both sides. 144 = x

  11. Check It Out! Example 3c Solve the equation. Check your answer. Multiply both sides by 5. Square both sides. Divide both sides by 4. x = 100

  12. Check Example 4A: Solving Radical Equations with Square Roots on Both Sides Solve the equation. Check your answer. Square both sides. 2x – 1 = x + 7 Add 1 to both sides and subtract x from both sides. x = 8 

  13. Add to both sides. Example 4B: Solving Radical Equations with Square Roots on Both Sides Solve the equation. Check your answer. Square both sides. 5x – 4 = 6 Add 4 to both sides. 5x = 10 Divide both sides by 2. x = 2

  14. Squaring both sides of an equation may result in an extraneous solution—a number that is not a solution of the original equation. Suppose your original equation is x = 3. x = 3 x2 = 9 Square both sides. Now you have a new equation. Solve this new equation for x by taking the square root of both sides. x = 3 or x = –3

  15. Example 5A: Extraneous Solutions Solve Check your answer. Subtract 12 from each sides. Square both sides 6x = 36 Divide both sides by 6. x = 6

  16. Check Example 5A Continued Solve Check your answer. Substitute 6 for x in the equation.  18 6 6 does not check. There is no solution.

  17. 5 Substitute 5 for l, 15 for A and for w. Check It Out! Example 6 A rectangle has an area of 15 cm2. Its width is 5 cm, and its length is ( ) cm. What is the value of x? What is the length of the rectangle? A = lw Use the formula for area of a rectangle. Divide both sides by 5.

  18. 5 The value of x is 8. The length of the rectangle is cm. Check It Out! Example 6 Continued A rectangle has an area of 15 cm2. Its width is 5 cm, and its length is ( ) cm. What is the value of x? What is the length of the rectangle? Square both sides. 8 = x

  19. 5 Check A = lw Check It Out! Example 6 Continued A rectangle has an area of 15 cm2. Its width is 5 cm, and its length is ( ) cm. What is the value of x? What is the length of the rectangle? Substitute 8 for x.  15 15

  20. Lesson Quiz: Part I Solve each equation. Check your answer. 1. 2. 36 45 no solution 3. 4. 11 5. 4 6. 4

  21. 7. A triangle has an area of 48 square feet, its base is 6 feet and its height is feet. What is the value of x? What is the height of the triangle? Lesson Quiz: Part II 253; 16 ft

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